Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise

doi:10.1016/j.cam.2017.04.050

	Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise
	Zhou, Weien 1; Zhang, Jingjing 3; Hong, Jialin4 ; Song, Songhe 1,2
	2017-12-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	325 页码:134-148
摘要	In this paper, we construct stochastic symplectic Runge Kutta (SSRK) methods of high strong order for Hamiltonian systems with additive noise. By means of colored rooted tree theory, we combine conditions of mean-square order 1.5 and symplectic conditions to get totally derivative free schemes. We also achieve mean-square order 2.0 symplectic schemes for a class of second-order Hamiltonian systems with additive noise by similar analysis. Finally, linear and non-linear systems are solved numerically, which verifies the theoretical analysis on convergence order. Especially for the stochastic harmonic oscillator with additive noise, the linear growth property can be preserved exactly over long-time simulation. (C) 2017 Elsevier B.V. All rights reserved.
关键词	Stochastic differential equations Stochastic Runge-Kutta methods Symplectic integrators Mean-square convergence
DOI	10.1016/j.cam.2017.04.050
语种	英语
资助项目	HPCL ; NSFC[11501570] ; NSFC[11571366] ; NSFC[11201125] ; NSFC[91130003] ; NSFC[11021101] ; NSFC[11290142] ; NSFC[91530018] ; foundation of department of education of Henan province[12B110010] ; young growth foundation of Henan Polytechnic university[B2390]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000404308000010
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25815
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Weien
作者单位	1.Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China 2.Natl Univ Def Technol, State Key Lab High Performance Comp, Changsha 410073, Hunan, Peoples R China 3.East China Jiaotong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China 4.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhou, Weien,Zhang, Jingjing,Hong, Jialin,et al. Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2017,325:134-148.
APA	Zhou, Weien,Zhang, Jingjing,Hong, Jialin,&Song, Songhe.(2017).Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,325,134-148.
MLA	Zhou, Weien,et al."Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 325(2017):134-148.